Use Tarjan's low-link technique to find every bridge (critical edge) and articulation point (cut vertex) in an undirected graph in O(V + E). The interview pattern behind LeetCode 1192 Critical Connections, asked at Google, Meta, and Amazon.
Master the Floyd-Warshall algorithm: a triple-nested DP that computes shortest paths between every pair of vertices in O(V^3), supports negative edges, and detects negative cycles. The interview workhorse for dense graphs and small V, asked at Google, Amazon, and Microsoft.
Master Bellman-Ford: relax every edge V-1 times to compute single-source shortest paths even with negative edges, and detect negative cycles in one extra pass. The algorithm behind LeetCode 787 Cheapest Flights Within K Stops, asked at Google, Amazon, and Meta.
Master A* search: a heuristic-guided best-first search that finds optimal shortest paths far faster than Dijkstra by combining actual distance g(n) with an admissible estimate h(n). The interview pattern behind LeetCode 1091 Shortest Path in Binary Matrix and the algorithm powering Google Maps, game AI, and robotics navigation.